cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 10 results.

A047101 Sum{T(i,n-i): i=0,1,...,n}, array T as in A047100.

Original entry on oeis.org

1, 2, 3, 5, 10, 20, 37, 70, 140, 280, 544, 1065, 2130, 4260, 8418, 16684, 33368, 66736, 132760, 264436, 528872, 1057744, 2110233, 4212350, 8424700, 16849400, 33658512, 67254158, 134508316, 269016632, 537715716, 1074932056, 2149864112
Offset: 0

Views

Author

Clark Kimberling

Keywords

A047102 T(n,n), array T as in A047100.

Original entry on oeis.org

1, 1, 3, 11, 37, 131, 481, 1778, 6637, 25010, 94819, 361275, 1382507, 5309449, 20452432, 78991548, 305779341, 1186056909, 4608647096, 17936112649, 69903546693, 272788289379, 1065751393409, 4168163479770, 16317475606787
Offset: 0

Views

Author

Clark Kimberling

Keywords

A047103 T(n,n-1), array T as in A047100.

Original entry on oeis.org

1, 1, 5, 16, 58, 220, 821, 3090, 11743, 44792, 171495, 659051, 2540116, 9814642, 38007320, 147472450, 573200298, 2231386904, 8698569320, 33952074197, 132672190652, 518973027214, 2031995088017, 7963057824045, 31231061046115
Offset: 1

Views

Author

Clark Kimberling

Keywords

A047104 T(n,n-2), array T as in A047100.

Original entry on oeis.org

1, 2, 5, 21, 89, 340, 1312, 5106, 19782, 76676, 297776, 1157609, 4505193, 17554888, 68480902, 267420957, 1045329995, 4089922224, 16015961548, 62768643959, 246184737835, 966243694608, 3794894344275, 14913585439328
Offset: 2

Views

Author

Clark Kimberling

Keywords

A047105 T(n,n-3), array T as in A047100.

Original entry on oeis.org

1, 3, 5, 31, 120, 491, 2016, 8039, 31884, 126281, 498558, 1965077, 7740246, 30473582, 119948507, 472129697, 1858535320, 7317392228, 28816569762, 113512547183, 447270667394, 1762899256258, 6950527615283, 27412071431285
Offset: 3

Views

Author

Clark Kimberling

Keywords

A047106 T(n,n+1), array T as in A047100.

Original entry on oeis.org

1, 2, 6, 21, 73, 261, 957, 3547, 13267, 50027, 189780, 723456, 2769333, 10637790, 40984228, 158306891, 612856611, 2377260192, 9237543329, 35951472496, 140116098727, 546778366195, 2136168391753, 8354417782742, 32705042089703
Offset: 0

Views

Author

Clark Kimberling

Keywords

A047107 T(n,n+2), array T as in A047100.

Original entry on oeis.org

1, 3, 10, 36, 130, 476, 1769, 6630, 25017, 94961, 362181, 1386826, 5328341, 20531796, 79315343, 307077270, 1191203283, 4628896233, 18015359847, 70212552034, 273990076816, 1070416998344, 4186254302972, 16387566482916
Offset: 0

Views

Author

Clark Kimberling

Keywords

A047108 T(n,n+3), array T as in A047100.

Original entry on oeis.org

1, 4, 15, 57, 215, 812, 3083, 11750, 44934, 172401, 663370, 2559008, 9894006, 38331115, 148770379, 578346672, 2251636041, 8777816518, 34261079538, 133873978089, 523638632149, 2050085911219, 8033148700174, 31502487793694
Offset: 0

Views

Author

Clark Kimberling

Keywords

A047109 T(2n,n), array T as in A047100.

Original entry on oeis.org

1, 1, 5, 31, 151, 917, 5619, 33627, 210911, 1326395, 8366161, 53441835, 342477957, 2203613164, 14248253995, 92379163952, 600644552471, 3915699367751, 25579440322831, 167423682425912, 1097738520430457, 7208383257398805
Offset: 0

Views

Author

Clark Kimberling. Definition revised Dec 08 2006

Keywords

Extensions

Name corrected by Sean A. Irvine, Jan 12 2025

A047120 Array T read by diagonals: T(h,k)=number of paths consisting of steps from (0,0) to (h,k) such that each step has length 1 directed up or right and touches the line y=x/4 only at lattice points.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 3, 1, 1, 1, 4, 6, 4, 2, 1, 1, 5, 10, 10, 6, 3, 1, 1, 6, 15, 20, 16, 6, 4, 1, 1, 7, 21, 35, 36, 22, 6, 5, 1, 1, 8, 28, 56, 71, 58, 28, 6, 6, 1, 1, 9, 36, 84, 127, 129, 86, 34, 12, 7, 1, 1, 10, 45, 120, 211, 256, 215, 120, 46, 19, 8, 1
Offset: 0

Views

Author

Clark Kimberling

Keywords

Crossrefs

Cf. A047089 (with y=x/2), A047100 (with y=x/3).

Programs

  • Mathematica
    T[, 0] = 1; T[0, ] = 1; T[h_, k_] := T[h, k] = If[k-1 >= h/4 || k <= h/4, T[h, k-1], 0] + T[h-1, k];
Table[T[h - k, k], {h, 0, 11}, {k, h, 0, -1}]  // Flatten (* Jean-François Alcover, Mar 06 2019 *)
Showing 1-10 of 10 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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